(Nearly) Optimal Time-dependent Hamiltonian Simulation

TL;DR

This paper introduces a simple quantum algorithm for simulating time-dependent Hamiltonians with near-optimal scaling, improving efficiency and extending applications to lattice and Floquet systems, and enabling new quantum phase transition studies.

Contribution

The paper presents a new quantum algorithm extending quantum signal processing for time-dependent Hamiltonian simulation with near-optimal scaling and broad applications.

Findings

Achieves optimal or near-optimal scaling in simulation parameters.

Provides efficient simulation methods for lattice and Floquet systems.

Enables studying quantum phase transitions on quantum computers.

Abstract

We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly optimal in inverse of error tolerance, which could be improved to optimal scaling under certain input models. As applications, we discuss the problem of simulating generalized lattice system and time-periodic, or Floquet system, showing that our framework provides a neater yet highly efficient solution, achieving optimal/nearly optimal scaling in all parameters. In particular, our method also paves a new way for studying phase transition on quantum computer, extending the reach of quantum simulation.